Frobenius扩张下的丁投射(内射)模

Ding Projection(Injection)Modle under Frobenius Expansion

证明在任意结合环R上,若环扩张RA是Frobenius扩张,对于Frobenius扩张下的丁投射模,任意的左A-模M是丁投射的当且仅当作为左R-模时M是丁投射的,并且探讨了Frobenius扩张下模的丁投射维数的相关性质。类似地,给出了Frobenius扩张下丁内射模的相关性质。

This paper proved that on an arbitrary associative ring R,if ring expansion R∈A is Frobenius expansion,for the Ding projection module under Frobenius expansion,any left A-modle M is Ding projection,and M is Ding projection only when it is left R-modle.In addition,the related properties of the Ding projection dimension of modle under Frobenius expansion were discussed.Similarly,the related properties of the Ding injection modle under Frobenius expansion were also provided.